Теоретическое моделирование теплопроводности материалов (Theoretical Simulations of Thermal Conductivity of Materials) тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Зераати Маджид

• Зераати Маджид
• кандидат наук
• 2025

Оглавление диссертации кандидат наук Зераати Маджид

Contents

Page

Introduction

Chapter 1. Background

1.1 Introduction of thermal conductivity

1.1.1 Why is it essential to study thermal conductivity?

1.2 Thermal barrier coatings: an overview

1.2.1 Introduction and history

1.2.2 Experimental aspects of thermal barrier coatings

1.2.3 Limitations of traditional materials

1.2.4 Future directions

Chapter 2. Density Functional Theory and Machine Learning

Potentials

2.1 Density functional theory

2.1.1 Schrodinger equation

2.1.2 Born-Oppenheimer approximation

2.1.3 Hartree-Fock approximation

2.1.4 Density functional theory

2.1.5 Hellmann-Feynman theorem

2.2 Machine learning interatomic potentials

2.2.1 Essential concepts of machine learning interatomic potentials

2.2.2 Data collection

2.2.3 Descriptors

2.2.4 Moment tensor potentials and active learning

2.2.5 Neuroevolution machine learning potentials (NEP)

Chapter 3. Methods for Computing Thermal Conductivity and

Related Properties

3.1 Phononic thermal conductivity

3.2 Phonon

3.3 Lattice dynamics and the dynamical matrix

Page

3.4 Quantum theory of lattice vibrations

3.5 Phononic specific heat

3.6 Boltzmann transport equation

3.6.1 Variational principle

3.6.2 Relaxation time approximation (RTA)

3.7 Solving Boltzmann transport equation

3.7.1 Intrinsic scattering processes (three-phonon processes)

3.8 Effective harmonic model (EHM)

3.9 Equilibrium molecular dynamics (EMD)

3.10 Homogeneous non-equilibrium molecular dynamics (HNEMD)

3.10.1 Derivations based on linear-response theory for general many-body potentials

3.10.2 Equation of motion in HNEMD

3.10.3 Quantum correction of thermal conductivity in HNEMD

3.11 Thermal expansion coefficient (TEC)

3.12 Path-Integral Molecular Dynamics in GPUMD

3.13 Elastic constants and mechanical properties

Chapter 4. High-Throughput Screening for Thermal Barrier

Coatings

4.1 Overview of high-throughput screening

4.2 Materials-Space exploration using machine learning

4.2.1 Advantages

4.2.2 Challenges

4.3 Accelerating thermal conductivity simulations

4.3.1 Computational methods

4.3.2 Advantages

4.3.3 Challenges

4.4 Conclusion

Chapter 5. Searching for Promising Materials for Thermal

Barrier Coatings I

5.1 Machine learning potentials

5.2 Comparison of methods for computing thermal conductivity

Page

5.3 Results for thermal conductivity

5.4 Results for thermal expansion coefficient

5.5 Mechanical properties of promising materials

5.6 Some practical aspects

Chapter 6. Searching for Promising Materials for Thermal

Barrier Coatings II

6.1 Machine learning potentials

6.2 Results for thermal expansion coefficient

6.3 Results for thermal conductivity

6.3.1 The effect of disorder on thermal conductivity

6.4 Elastic constants and mechanical properties

6.5 Selecting materials for TBC application

6.6 Conclusions

Chapter 7. Gehlenite as a Potential Material for Thermal Barrier

Coatings

7.1 Theoretical results

7.2 Sample preparation

7.3 Thermal cycling tests of deposited gehlenite samples

7.4 Concluding remarks for gehlenite

Conclusions

Acknowledgments

List of symbols and abbreviations

Bibliography

List of Figures

List of Tables

Введение диссертации (часть автореферата) на тему «Теоретическое моделирование теплопроводности материалов (Theoretical Simulations of Thermal Conductivity of Materials)»

Introduction

Relevance of the work. Since thermal barrier coatings (TBCs) are vital components in the aerospace, energy, and high-temperature-related industries. Serving as protective layers on the surfaces of components made of metals, ceramics, or composites, these coatings prevent damages caused by high temperatures and heat transfer to other parts of the system. With the increasing demand for performance and durability in high-temperature conditions, the importance of developing and optimizing thermal barrier coatings has grown significantly.

Currently, the main material used for TBCs is yttria stabilized zirconia (YSZ), due to its stability at high temperatures, oxidation, erosion and corrosion resistance, and desirable thermophysical properties. YSZ is a ceramic material composed of zirconia (ZrO2) with 6-8 wt.% yttria (Y2O3). Its low thermal conductivity 2 W/(m.K) at 1273 K), a high linear TEC (11x10-6 K-1 at 293-1273 K), good thermal shock resistance, and excellent chemical stability make it an ideal choice for TBCs [1]. The disadvantages of these coatings include phase transition at 1150-1200 °C and high oxygen conductivity limiting the number of thermal cycles and operating temperature at 1200 °C for YSZ.

During the 2000s, calcium magnesium aluminosilicates (CMAS) were utilized in high-temperature testing with YSZ coatings [2]. These silicates do not withstand temperatures greater than 1200 °C, infiltrate the TGO and fracture the TBC, and therefore, it experiences detachment and fails when the ceramic cools [3; 4].

Finding new materials for TBCs is crucial. New materials with features such as low heat transfer capability, suitably high TEC, high phase, and thermal, mechanical, and chemical stability in dusty air could improve the performance and efficiency of these coatings. Additionally, developing materials with lower weight and better thermophysical properties can reduce the overall weight of gas turbines and enhance the efficiency and application of thermal coatings. These materials can also provide higher resistance to mechanical damage from impact, pressure, and vibrations, leading to a decrease in failures and an increase in the useful life of components. Furthermore, considering different environmental conditions, new materials with greater resistance to oxidation can extend the useful life of the coating. Therefore, research and development in finding new materials for thermal barrier

coatings are of great importance and can contribute to improving the performance and durability of systems utilizing these coatings.

Dissertation goals. This research aims is devoted to investigation into the thermal conductivity and mechanical properties of various materials, aimed at identifying promising candidates for TBCs in high-temperature applications. Using advanced computational techniques, including molecular dynamics simulations, the Boltzmann transport equation, and machine learning potentials.

Scientific novelty. The scientific novelty is built up from the following results:

1. We implemented a reliable high-throughput screening for TBCs. This method included several important properties of TBCs.

2. For the first time, we identified several materials that stand out for their potential as TBCs.

Theoretical and practical significance. This innovative approach has the potential to greatly advance the theoretical study of TBCs. The results obtained are closely aligned with the pressing challenges associated with the development of new TBC materials that exhibit exceptional performance, as discussed in the dissertation.

Research methodology. To achieve the aforementioned goals, the methodology and methods of the present research were identified and the dissertation work was aimed at solving the following tasks, which correspond to the main dissertation chapters:

1. Comparison of currently thermal barrier coating materials with YSZ and highlights the advantages and disadvantages of them;

2. The selection of the proper high-throughput screening methods for thermal barrier coatings;

3. Comparison of methods for computing thermal conductivity and related properties;

4. Training machine learning interatomic potentials for candidate materials;

5. Using advanced computational techniques based on the CPU and GPU packages to calculate thermophysical properties such as thermal conductivity, thermal expansion, elastic properties, etc.;

6. Validation of theoretical methods with available experimental data.

7. Employ specific selection criteria to narrow down the list of candidate materials;

8. Validate our finding candidates in experiment, like as gehlenite.

Propositions for defense.

1. Comparison of methods for computing thermal conductivity. To analyze our theoretical methods for thermal conductivity, the author compared different computational methods and related physics. Specifically, the author focused on La2Zr2O7, Mg3Àl2(SiO4)3, ZrSiO4, and BaZrO3, and compared results of different methods with experimental data. These materials have been well-studied theoretically and experimentally with reliable results.

2. For the first time, the author identified several materials that stand out for their potential as TBCs.

3. The author examined gehlenite, Ca2Al2SiO7 as a possible TBCs candidate. From his results it is clear that gehlenite could be a potential component for improved TBCs. There are several possible avenues. First, it can be used as the second (top) layer in the preparation of TBCs. Second, it can be used as a component of promising TBC composite systems providing high porosity of the ceramics and, therefore, low thermal conductivity.

Validation of the research results, reliability. The dissertation work was performed at the high scientific level. The reliability of the results is ensured by the use of a wide range of experimental data against simulations. Through this study, we identified several materials that stand out for their potential as TBCs.

The statements and conclusions formulated in the dissertation have received qualified approbation at international scientific conferences. The credibility is also confirmed by the publication of research results in peer-reviewed scientific journals.

The main results of the dissertation were reported at the following scientific conferences:

1. Majid Zeraati, Artem R. Oganov; "Strongly Anharmonic Phonons in Pyrope"; Recent Progress in Thermal Transport Theory and Experiments, ICTP, Italy, (2022) (Best Poster).

2. Majid Zeraati, Artem R. Oganov; "Calculation of Thermal Conductivity of Materials from First Principles"; Thermal Management Workshop, Minsk, Belarus, (2023).

3. Majid Zeraati, Artem R. Oganov; "Searching for low thermal conductivity materials for thermal barrier coatings"; 1st Open BRICS Conference on Smart Materials and Devices 2024, Shenzhen, China, (2024) (Best Student Talk).

The materials of the dissertation are fully presented in the two published works in the peer-reviewed journals.

Dissertation structure. The dissertation consists of an introduction, 6 chapters, and a conclusion. The dissertation is 170 pages long, including 43 figures, and 18 tables. The list of references contains 210 titles.

Заключение диссертации по теме «Другие cпециальности», Зераати Маджид

Conclusion

In conclusion, this study presents a thorough investigation into the thermal conductivity and mechanical properties of various materials, aimed at identifying promising candidates for TBCs in high-temperature applications. Using advanced computational techniques, including molecular dynamics simulations, the Boltz-mann transport equation, and machine learning potentials, we calculated the thermal conductivity of several candidate materials up to 1500 K. By analyzing the temperature dependence of these materials and factoring in anharmonic effects, we found that the behavior of thermal conductivity at high temperatures deviates from the commonly assumed inverse proportionality to temperature. Our methodology, validated against experimental data, allowed us to identify materials that exhibit the most desirable properties for use in TBCs.

One of the primary goals of this study was to determine materials with low thermal conductivity, high thermal expansion coefficients, and suitable mechanical properties, including fracture toughness and elastic modulus. To systematically narrow down the list of candidate materials, we employed specific selection criteria. First, we set a thermal conductivity threshold of 2 W/(m-K) at 1000 K. Next, we applied a range of (3.0 — 5.0) x 10-5 K-1 for average volumetric thermal expansion coefficients from 700 K to 1300 K. These thresholds allowed us to eliminate materials that did not meet the required thermal performance standards. We also applied Pugh's ratio, a measure of ductility, with a maximum limit of 0.57 to ensure that selected materials exhibit sufficient mechanical resilience. Fracture toughness values greater than 1 MPa-m1/2 were another essential criterion, as this property is vital for withstanding high-stress environments, particularly in the presence of erosion and other mechanical stresses.

Through this rigorous selection process, we identified several materials that stand out for their potential as TBCs. These materials presented in Table 18.

These materials were selected based on their low thermal conductivity at high temperatures, thermal expansion coefficients within the specified range, and mechanical properties that ensure durability under harsh operating conditions. Additionally, many of these materials exhibited high resistance to CMAS corrosion, which is a critical factor in the degradation of traditional TBCs.

Table 18 — Thermal conductivity (at T = 1500 K), volumetric thermal expansion (at T = 1500 K), Pugh's ratio, and fracture toughness of selected materials for TBCs application.

Thermal TEC Pugh's Fracture

Compound (structure) conductivity 10-5 toughness

[W/(m-K)j [K-1] Ratio [MPa-m1/2]

Perovskite

CaZrO3* (perovskite) 1.62±0.09 4.16 0.53 1.72

SrBa2MgNb2Ogt (trigonal double perovskite) 1.43±0.08 4.20 0.53 1.31

Ba3YTiTaOg* (trigonal double perovskite) 1.37±0.07 3.80 0.54 1.29

Ba2YNbO6 (double perovskite) 1.36±0.07 3.85 0.54 1.26

Ba2YTaO6 (double perovskite) 1.32±0.08 3.50 0.57 1.27

Sr3LaTa3O12 (layered perovskite) 1.10±0.10 4.87 0.49 1.09

BaLaMgNbO6 (double perovskite) 1.14±0.09 5.40 0.48 0.75

BaLaMgTaO6 (double perovskite) 1.11±0.10 5.16 0.26 1.61

Ba3LaTa3Oi2 (layered perovskite) 0.84±0.09 3.10 0.57 1.08

Garnet

Gd3Sc3Al3O12 (garnet) 1.58±0.05 3.69 0.51 1.44

Ca2YZr2Àl3Oi2 (garnet) 1.41±0.05 3.66 0.50 1.21

Sr3Y2Ge3O12 (garnet) 1.30±0.08 3.58 0.44 0.92

Gd3Ga5Oi2 (garnet) 1.16±0.08 4.43 0.48 1.37

Ca3Y2Ge3Oi2 (garnet) 1.16±0.06 3.68 0.43 0.88

Gd3Sc2Ga3O12 (garnet) 1.00±0.07 7.29 0.43 0.84

Pyrochlore

Y2Ti2O7 (cubic pyrochlore) 1.76±0.05 3.56 0.49 2.27

Gd2Ti2O7 (cubic pyrochlore) 1.41±0.07 4.27 0.50 1.69

La3Mg2Ta3Oi4* (trigonal ordered pyrochlore) 1.32±0.04 3.15 0.54 1.56

La3Mg2Nb3Oi4^ (trigonal ordered pyrochlore) 1.27±0.07 3.35 0.50 1.49

La3Ca2Nb3Oi4 (trigonal ordered pyrochlore) 1.24±0.06 3.40 0.51 1.32

Gd2Zr2O7 (cubic pyrochlore) 1.19±0.07 3.98 0.50 1.64

Gd2Hf2O7 (cubic pyrochlore) 1.00±0.05 3.05 0.55 1.70

Others

CaLaAl3O7 (melilite) 1.46±0.16 3.25 0.47 1.03

Ba6Ti2NbsO30 (tetragonal tungsten bronze) 1.12±0.10 5.43 0.46 0.85

Y4Ca(SiO4)3O (apatite) 1.04±0.05 4.02 0.43 0.88

Gd2AlTaO7* (weberite) 1.19±0.09 4.69 0.43 0.79

La3TaO7 (distorted weberite) 1.08±0.07 4.11 0.50 1.13

8% YSZ (Exp. at t = 1000 K) -2.0 [131] -3.21 [160] - 1.49 [209]

8% YSZ (Theory. at t = 1000 K) 2.24±0.13 4.06

10% YSZ (Exp.) [210] 1.9 <100> 1.1 <110>

t Hypothetical compounds.

* Known compound, hypothetical compounds.

* Has phase transition to cubic perovskite at 2023 K.

Among the materials evaluated, gehlenite (Ca2Al2SiO7) emerged as a particularly promising candidate due to its excellent thermal and mechanical properties. Its low thermal conductivity, high thermal expansion coefficient, and resistance to CMAS corrosion make it an attractive alternative to conventional YSZ. While gehlenite requires a protective YSZ layer to prevent reactions with metal substrates, it has demonstrated exceptional potential as a top layer in multilayer TBC systems. Additionally, solid solutions within the gehlenite-akermanite series and other structural analogs offer pathways for further optimizing the properties of TBC materials.

The overall contribution of this research lies in the identification of these promising materials and the establishment of a robust methodology for evaluating their suitability for TBC applications. By combining advanced computational techniques with stringent selection criteria, we were able to pinpoint materials that exhibit superior performance in terms of thermal conductivity, thermal expansion, and mechanical resilience. These findings contribute to ongoing efforts to improve the efficiency and durability of thermal barrier coatings, paving the way for more reliable high-temperature materials in industrial applications.

Future work should focus on experimental validation of the selected materials, particularly in real-world operating environments. Such validation will be critical for transitioning these materials from theoretical candidates to practical, deployable solutions in aerospace, power generation, and other high-temperature industries. Additionally, further exploration of composite systems and the fine-tuning of material properties through solid solutions and structural modifications could lead to even more advanced TBCs capable of withstanding the extreme conditions encountered in modern technological applications.

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